The above statements, however, have by no means exhausted the
possibilities. For it has been tacitly assumed that in the combination
of several things the _sequence_ according to which this combination
takes place should not condition a difference of the result. This is
true of a number of things, but not of all. In order, therefore, to
exhaust the possibilities the theory of combinations must be extended
also to cases in which the sequence is to be taken account of, so that
the form ab is regarded as different from ba.
We will not undertake to work out the results of this assumption. It is
obvious that the manifoldness of the various cases is much greater than
if we neglect the sequence. On this point we have one more observation
to make, that further causes for diversity exist. It is true that a
chemical combination is not influenced by the sequence in which its
elements enter the combination, but there do occur with the same
elements differences in their _quantitative relations_, and thereby a
new complexity is introduced into the system, so that two or more
similar elements can form different combinations according to the
difference in the quantitative relations. Still, even with this, the
actual manifoldness is not exhausted, for from the same elements and
with the same quantitative relations there can arise different
substances called _isomeric_, which, for all their similarity, possess
different energy contents. But the first scheme is not demolished, nor
does it become impracticable because of this increase of manifoldness.
What simply happens is that _several_ different things instead of one
appear in the same group of the original scheme, the systematic
classification of which necessitates a further schematization by the use
of other characteristics.
=24. Arrangement of the Members.= Since we have started from the
proposition that all members of a group are different from one another,
we have perfect liberty to arrange them. The most obvious arrangement
according to which some _one_ definite member is followed by a _single_
other member and so forth (as, for example, the arrangement of the
letters of the alphabet) is by no means the only mode of arrangement,
though it is the simplest. Besides this _linear_ arrangement, there is
also, for instance, the one in which two new members follow
simultaneously upon each previous one, or the members may be disposed
like a number of balls heaped up in a pyramid. However, we shall not
have much occasion to occupy ourselves with these complex types of
arrangement, and can therefore limit our considerations at first to the
simplest, that is, to the linear arrangement.
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